{"id":8846,"date":"2012-04-26T03:43:19","date_gmt":"2012-04-26T02:43:19","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=8846"},"modified":"2022-01-30T00:42:40","modified_gmt":"2022-01-30T00:42:40","slug":"a-figura-representa-parte-da-representacao-grafica-da-funcao-f","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=8846","title":{"rendered":"A figura representa parte da representa\u00e7\u00e3o gr\u00e1fica da fun\u00e7\u00e3o $f$"},"content":{"rendered":"<p><ul id='GTTabs_ul_8846' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_8846' class='GTTabs_curr'><a  id=\"8846_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_8846' ><a  id=\"8846_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_8846'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag128-12.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignright\" title=\"Gr\u00e1fico\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag128-12.png\" alt=\"\" width=\"486\" height=\"400\" \/><\/a>A figura representa parte da representa\u00e7\u00e3o gr\u00e1fica da fun\u00e7\u00e3o $f$ deriv\u00e1vel em $\\mathbb{R}$.<br \/>\nAs retas ${t_1}$ e ${t_2}$ s\u00e3o tangentes ao gr\u00e1fico de $f$ nos pontos B e A, respetivamente.<\/p>\n<p>Recorrendo ao gr\u00e1fico:<\/p>\n<ol>\n<li>Resolva a equa\u00e7\u00e3o $f'(x) = 0$ em $\\left[ { &#8211; 2,3} \\right]$.<\/li>\n<li>Determine o valor de $$\\mathop {\\lim }\\limits_{x \\to 2,5} \\frac{{f(2,5 + h) &#8211; 0,02}}{h}$$<\/li>\n<li>Determine $f'(0)$ e a equa\u00e7\u00e3o reduzida da reta ${t_1}$.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8846' onClick='GTTabs_show(1,8846)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_8846'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag128-12.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignright\" title=\"Gr\u00e1fico\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag128-12.png\" alt=\"\" width=\"486\" height=\"400\" \/><\/a>Como\u00a0${x =\u00a0 &#8211; \\frac{1}{2}}$ e ${x = 2}$ s\u00e3o, respetivamente, maximizante e minimizante de $f$, tem-se: $$\\begin{array}{*{20}{c}}<br \/>\n{f'(x) = 0}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}<br \/>\n{x =\u00a0 &#8211; \\frac{1}{2}}&amp; \\vee &amp;{x = 2}<br \/>\n\\end{array}}<br \/>\n\\end{array}$$<\/li>\n<li>Como a reta ${t_2}$ \u00e9 tangente ao gr\u00e1fico de $f$ no ponto A, tem-se: $$f'(2,5) = \\mathop {\\lim }\\limits_{h \\to 0} \\frac{{f(2,5 + h) &#8211; 0,02}}{h} = {m_{{t_2}}} = \\frac{3}{2}$$<\/li>\n<li>Como a reta ${t_1}$ \u00e9 tangente ao gr\u00e1fico de $f$ no ponto B, tem-se: $$f'(0) = {m_{{t_1}}} = \\frac{{3 &#8211; 1}}{{ &#8211; 1 &#8211; 1}} =\u00a0 &#8211; 1$$ sendo $y =\u00a0 &#8211; x + 2$ a equa\u00e7\u00e3o reduzida da reta ${t_1}$.<\/li>\n<\/ol>\n<p><strong>Nota<\/strong>: Ainda que o exerc\u00edcio esteja inclu\u00eddo no tema das fun\u00e7\u00f5es trigonom\u00e9tricas, esclarece-se que a fun\u00e7\u00e3o $f$ \u00e9 polinomial c\u00fabica.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_8846' onClick='GTTabs_show(0,8846)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A figura representa parte da representa\u00e7\u00e3o gr\u00e1fica da fun\u00e7\u00e3o $f$ deriv\u00e1vel em $\\mathbb{R}$. As retas ${t_1}$ e ${t_2}$ s\u00e3o tangentes ao gr\u00e1fico de $f$ nos pontos B e A, respetivamente. Recorrendo&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21107,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,295],"tags":[427,293],"series":[],"class_list":["post-8846","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-12--ano","category-aplicando","category-funcoes-seno-co-seno-e-tangente","tag-12-o-ano","tag-funcao-derivada"],"views":4168,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12V3Pag129-12_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8846","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=8846"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8846\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21107"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8846"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8846"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8846"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=8846"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}